The moons are not usually associated with the Daedra, but it seems that there are at least two three instances where this is not the case.

The first case is the Bloodmoon, where Hircine causes Secunda to become red during the time of his hunt.

The second case is less obvious, it's http://www.uesp.net/wiki/Lore:Heavy_Armor_Repairthat Daedric armor seems to have slightly different properties depending on the Moons, that it's best repaired under a full or new moon, but never during an eclipse.

Edit: Of course, there's also Azura and the whole moon-and-star angle. :facepalm: I wonder which moon it's referring to.

Anyone got any other information regarding these connections?

From what I've read about on khajiit lore, the Moons are Nirn's deflector shields, keeping out the forces of Oblivion. But then again, the amulet of kings also does that...
Maybe the moons are not an entirely failsafe protection, and weakest in their protection when they are full, thus aiding in the repair of Daedric armor, but under an Eclipse they are at their strongest, so the daedric spirits of the armor can't be removed.

The bloodmoon thing, I guess, could be a natural waning of Secunda's power, which Hircine takes advantage of to host his hunt, and thus the two are linked...

But this is just Wild Mass Guessing.

Lorkhan was a Padomaic and his body became the moons. The only moon we know of is in fact a Daedra.

There's the wandering planet/moon, Ibar Daan (Did I spell that right?). It's the one floating above Vivec city.

The Khajiit are bound to the Lunar Lattice... which I suppose are the two moons, Lorkhan's body.

The TIL astronomy section mentions that parts of Masser and Secunda are dissolving/decomposing. What will happen to the Khajiit and the rest of Nirn?

I can understand Hircine and his lycanthropes, but it seems strange that Daedric armor, which would presumably usually be created by and imbued with the daedric servants of Mehrunes Dagon, would be affected by the moons.